Gather together numerous straight sticks that are no more than a quarter-inch thick. Ensure that they are all dry and not of a species that produces poisonous fumes when burned.
Stack the dry sticks in a loose cylindrical bundle of the same diameter as the desired internal diameter for the chimney. Bind the bundle with natural cord once it is the correct size, to prevent the sticks from separating. The result should be a bundle of sticks that stays together but has plenty of air gaps between individual sticks.
Stand the twig bundle upright at the back of the clay oven, where the chimney should be. Cover the bundle with dry grass to a depth of about a quarter-inch, holding it in place with more string if necessary.
Cover the entire bundle in a layer of stiff clay to a thickness of at least 4 inches. Attach the chimney to the open end of the clay oven, forming a continuous and air-tight seal between the two parts. Allow the chimney to dry for seven days before progressing to the next task.
Set a fire in the back of the oven, where the flames can catch the grass covering the bundle of sticks. Continue to feed the fire until the entire bundle of sticks has been consumed and the chimney is left as an empty cylinder.